Articles written in Sadhana

    • Modified fuzzy c-mean for custom-sized clusters


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      Fuzzy c-mean (FCM) is one of the widely used data clustering methods. FCM method not only divides a data set into several clusters but also determines the potential belongingness of each data in different clusters. The size of clusters generated by FCM cannot be controlled by the inherent mechanism. However,sometimes real life situations demand that the clusters should have some pre-specified size. In this study, the FCM method is further extended to obtain clusters with specified size. In the first step of the proposed method, FCM algorithm is executed; later the potential belongingness matrix passes through an optimization model to yield clusters with specified sizes. In the proposed technique, the centres of the clusters obtained from FCM are considered but the boundary elements are redistributed to achieve equal or custom-sized clusters. The methodology has been explained further with examples.

    • Solving the shortest path problem in an imprecise and random environment


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      This paper considers a shortest path problem in an imprecise and random environment. The edges in the network represent the approximate time required to cover the distance from one vertex to another vertex while the traffic conditions change randomly for each edge. The approximate time has been defined by using trapezoidal fuzzy number whereas the traffic conditions has been defined in linguistic term. Such type of network problem can be called as Fuzzy Stochastic Shortest Path Problem (FSSPP) in imprecise and random environment. In order to solve the model, a method has been proposed based on the Dijkstra’s algorithm and some numerous example have been solved to present its effectiveness

    • On the distribution-free continuous-review production-inventory model with service level constraint


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      In this article, we study a continuous-review production-inventory model that assembles lost sales and backorders with service level constraint. The study under consideration assumes that the distribution of demand during the lead-time is known partially. The objective of this paper is twofold. Firstly, the distributionfree procedure is applied to obtain a closed-form solution of optimal production quantity, re-order level and lead-time in the random framework. Secondly, considering demand as a fuzzy random variable, the procedure isextended to the fuzzy random framework in which an algorithm is proposed to find the optimal global solution. Two numerical examples are provided to illustrate the methods. Furthermore, sensitivity analysis is performed to present some managerial inferences

    • A Branch-and-Bound-based solution method for solving vehicle routing problem with fuzzy stochastic demands


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      In this paper, a capacitated vehicle routing problem (CVRP) with fuzzy stochastic demands has been presented. Discrete fuzzy random variables have been used to represent the demands of the customers. The objective of CVRP with fuzzy stochastic demands is to obtain a set of routes that originates as well as terminates at the source node and while traversing the route, the demands of all the customers present in the network are satisfied. The task here is to carry out all these operations with minimum cost. CVRP in imprecise and randomenvironment has been considered here, and an a priori route construction technique has been adopted for which Branch and Bound algorithm has been used. The recourse policy used in this work is reactive, i.e. recourse todepot is done only upon the occurrence of the failure. The delivery policy considered here is unsplit delivery. Demands of the customers are the only source of impreciseness and randomness in the problem under construction.Parametric graded mean integration representation (PGMIR) method has been used for the comparison purposes, whenever required. A numerical example with four customers has been solved to present the proposed methodology.

    • Graphical method to solve fuzzy linear programming


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      In this paper, the graphical method for solving linear programming is extended in fuzzy environment. Here, we dealt with the fully fuzzy linear programming (FFLP) which involves fuzzy constraints and fuzzy objective. Determining and visualizing the fuzzy feasible space in the geometrical space is one of the novel contributions of this study. Defining fuzzy constraints as fuzzy lines and finding the nature of the point of intersection between fuzzy lines are also studied. The fuzzy constraints divide the geometrical into fuzzy half planes. Intersection of such fuzzy half planes yields a fuzzy convex hull. The optimal solution of fuzzy linear programming problem is obtained at an extreme point of this fuzzy convex hull. The results obtained from the proposed method are compared with existing methodologies.

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